EliminMatr {MultiStatM}

Elimination Matrix

Description

Eliminates the duplicated/q-plicated elements in a T-vector of multivariate moments and cumulants.

Usage

EliminMatr(d, q, useSparse = FALSE)

Arguments

d

dimension of a vector x

q

power of the Kronecker product

useSparse

TRUE or FALSE.

Value

Elimination matrix of order \eta_{d,q} \times d^q= {d+q-1 \choose q}. If useSparse=TRUE an object of the class "dgCMatrix" is produced.

References

Gy. Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021. Section 1.3.2 Multi-Indexing, Elimination, and Duplication, p.21,(1.32)

See Also

Other Matrices and commutators: EliminIndx(), QplicIndx(), QplicMatr(), SymIndx(), SymMatr(), UnivMomCum()

Examples

x<-c(1,2,3)
y<-kronecker(kronecker(x,x),x)
## Distinct elements of y
z<-as.matrix(EliminMatr(3,3))%*%y
## Restore eliminated elements in z
as.vector(QplicMatr(3,3)%*%z)